Method and machine for finishing surfaces



July 23,1940. DRUMMQND 2208572 METHOD AND MACHINE FOR FINISHING SURFACESFiled Aug. 1, 1938 4 Sheets-Sheet l ROBERT SDRUMMOND INVENTOR l BY wLMIZZWW ATTORNEYS July 23, 1940. R. s. DRUMMOND METHOD AND MACHINE FORFINI SHING SURFACES Filed Aug. 1, 1938 4 Sheets-Sheet 2 :y/ Mam-INVENTOR ROBERT $.DRUMMOND WWW, M JMM L ATTORNEYS y .1940. R. s.DRUMMOND 2,208,572

METHonANn mcamm FOR FINISHING sunmcms Filed Aug. 1, 195a 4 Sheets-Sheets I FIG.3.

INVENTOR ROBERT 5. DR U MMOND R 'M/MW W ATTORNEYS July 23, 1940. R. s.DRUMMOND 2308,572-

METHOD AND MACHINE FOR FINISHING SURFACES Filed Aug. 1, 1938 4Sheets-Sheet! FIG.4.

INVENTOR ROBERT S.DRUMMONC BY I W 9/ fi'M ATTORNEYS Patented July23,1940

UNITED STATES METHOD AND MACHINE FOR FINISHING SURFACES Robert S.Drummond,.Detroit, Mich., assignor to National Broach & Machine Company,De-

troit, Mich, a corporation oi. Michigan Application August 1, 1938,Serial No. 222,488

14 Claims.

This invention relates to an improved method and machine for finishingsurfaces, and more particularly to a machine for finishing nonplanarsurfaces of revolution. This application is a continuation-in-part of mycopending' application entitled "Method of finishing surfaces andmachine and cutter therefor," Serial No. 124,790, filed February 8,1937.

.According to the teachings of the present invention, a work piecehaving a non-planar surface of revolution is adapted to be finished bycontacting the same with a. rotary cutter, the cutter also having anon-planar surface of revolution.

The axis of the cutter and the axis of the work piece are crossed sothat the surface of the cutter contacts the surface of the work pieceonly over a small area. Theoretically, this area of contact between thework piece and the cutter is a point and. results from the fact that thecontact between the work piece and the cutter is the contact between twocurved surfaces. The work piece and the tool are simultaneously rotated.Rotation of the tool without rotation of the work piece would cause ashallow scallop to be cut into the surface of the work piece. When thework piece is rotated simultaneously with the rotation of the tool, thisshallow scallop is extended around the surface of the work piece forminga shallow groove therein. Simultaneously with the rotatool, a furtherrelative movement is introduced between the work piece and the tool in adirection to distribute the cutting action axially of the.

work piece. By properly selecting the speed of rotation of the workpiece and by proportioning the relative movement between the tool andthe work piece thereto, this helical groove will be so formed thatadjacent convolutions overlap to a considerable extent. The overlappingof ad-- jacent convolutions of 4 the helical groove. will v normally beof suflicient extent so that the finished surface is extremely smooth.45 The type of cutting performed according to the teachings of thisinvention is entirely novel and presents a number of decided advantagesover methods previously practiced,as will be subsequently pointed out.Accordingly it is an object 5 of the present invention to practice a newmethod tion of the work piece and the rotation of the tween the tool andwork piece in a direction to distribute a finishing action over thesurface to be finished. More specifically, it is an object of thepresent invention to practice a new method of finishing cylindrical orconical surfaces on a work piece by rotating the work piece about itsaxis and simultaneously rotating the cylindrical or conical finishingtool in contact with the surface to be finished with the axis of thefinishing tool and work piece crossed so as to provide'a limited area 10of contact between the tool and the surface and to introduce a relativemovement between the tool and work piece in a direction to distributethe finishing action along the surface to be finished.

It is a further object of the invention to pro- 15 vide a novel machinefor practicing the method referred to.

Other objects of the invention will be apparent as the descriptionproceeds and when taken in conjunction with the accompanying drawings,wherein Fig. 1 is a fragmentary plan view of a machine for finishing asurface of revolution in which the tool and the work piece are insubstantially line contact;

Fig. 2 is a fragmentary plan view of a machine for finishing a surfaceof revolution in which the finishing tools are in true crossed axesrelationship and contact the surface of'revolution over a limited area;

Fig. 3 is a fragmentary front elevation of a machine illustrating adifferent embodiment of my invention;

Fig, 4 is afragmentary front elevation of a machine illustrating asomewhat different embodiment of my invention;

Fig. 5 is a diagrammatic view showing the rela-- tionship between thework piece and the tool;

Fig. 6 is a diagrammatic view showing the relationship between adifferent type of tool and the work piece.

Fig. '7 is a fragmentary section of a work piece.

In its broadest aspects thepresent invention relates to finishing anon-planar surface of revolution by contacting the same with a rotatingcutter with the axis of the cutter and-the work piece crossed so thatthe tool would cut a shallow scallop in the work piece. The "work pieceis simultaneously rotated so that the shallow scallops are extendedabout the periphery of the surface, forminga shallow groove therein.Simultaneously with the rotation of both the work piece and the tool,further relative feeding movement is introduced between the work pieceand tool which causes the groove to be extended about the work piece ina helical path. The speed of rotation of the work piece and the speedsof relative movement between the work piece and tool is such thatadjacent convolutions of the helical groove overlap to a substantialextent.

It will be appreciated that, the invention as thus far described may bepracticed with a cylindrical tool contacting a cylindrical work piece;with a conical tool contacting a cylindrical work piece; with acylindrical tool contacting a conical work piece; with a conical toolcontacting a' conical work piece; or by providing proper guiding meanswith a tool having a concave or convex working surface contacting a workpiece having a concave or convex surface of revolution.

It is an essential consideration in the present method of finishingsurfaces that the work piece and tool are in contact only over a limitedarea. This area may vary from the theoretical point contact to an areaof substantial size according to the depth of cut, but in all cases itis substantially less than is encountered in the conventional milling.Due to the relative smallness of the area of contact the pressurebetween the work and the tool is substantially reduced and there is acorrespondingly reduced tendency for the tool to deform the work whileperforming its finishing operation. I

The shavings removed in this type of cutting are relatively finehair-like shavings and it has been found that a surface may be finishedwith great rapidity without generating sufficient heat to discolor theshavings. The type of cutting performance may be compared to fiycutting, and the surface as finished by this type of operation isaccurately finished and exhibits almost mirror like appearance.

While this type of surface finishing,- as pointed out above, may bepracticed with a variety of cutting tools and is applicable to a.variety of shapes of surfaces to be finished, for purposes ofillustration I have shown themethod as practiced with conical andcylindrical'cutters and on cylindrical work pieces.

In Fig. 1 I have illustrated for purposes of comparison a machine inwhich a-somewhat dif-. ferent method of finishing surfaces is practiced.Thismethod is further set forth in the parent application referred toabove and will be but briefly described here. In Fig. 1 a frame In isprovided upon which is secured ,a power head stock Hdriventhrough'suitable gearing by a motor l2. The work piece W is driven fromthe power headstock by means of a conventional driving fixture l3 and ismounted for rotation between" the head stock II and a tail stock I4, thelatter being provided with a hand wheel l5 for clamping and releasingthe work. A car-' riage I5 is mounted on the table for translation in adirection parallel to the axis of the work piece and suitable means forautomatically moving the table l5 are provided. These means take theformof a depending threaded lug l6 carried by-the carriage cooperating witha threaded shaft l1 suitably journaled in the frame III. A motor I8 isadapted to rotate the threaded shaft I! so as to translate the carriageI 5' in a direction parallel to the axis of the work piece W.

A tool support I9 is secured to the carriage l5 and is mounted foradjustment thereon abou a vertical axis. Suitable. means (not shown) areprovided to clamp the support in adjusted posifrom the work piece.

of adjusting the tool so that it may contact the work piece in straightline contact.

A tool slide 20 is mounted on the support I9 for adjustment thereon inthe ways indicated at 2|. The slide 20 carries a depending threaded lug22 which cooperates with a threaded shaft 23 suitably journaled in theslide 20. The shaft 23 .is provided with a squared projecting portion 24for coaction with a crank or the like to adjust the slide relative tothe support.

The tool T is supported by a spindle received in the tool spindlebushing indicated at 25 and is adapted to be driven from the motor 26 bysuitable means such as a chain, belt or train of gears received withinthe protecting housing 21.

In operation, the motors II and 26 are simultaneously energized torotate the work W and the tool T. The motor is is also energized andwill cause a slow translation of the carriage IS in the direction of theaxis of the work piece. The tool T is fed to depth in the work piece bysuitable manipulation'of the shaft 23 and subsequent translation of thecarriage l5 distributes respects like that shown in Fig. 1, but operatesto perform an entirely different cutting action. In this machine a frame30 is provided which carries a power head stock 3| driven by the motor32 and adapted to rotate a work piece W through a conventional drivingadapter 33. A tail stock 34 isalso carried by the frame and is providedwith a hand wheel 35 for clamping and releasing the work piece W in themachine.

Mounted on the frame 30 for translation in a direction parallel to theaxis of the work piece, as in suitable ways indicated at 36, is acarriage 31 on which are mounted in the embodiment illustrated, twofinishing tools. The carriage 31 is provided with a depending threadedlug 38 which is adapted to cooperate with a threaded shaft 39 suitablyjournaled in the frame 30 and driven .by a motor 40. Rotation of themotor 40, as will be understood, causes a slow translation of thecarriage 31 on the frame. Carriage 31 is provided with two tool supports4|. These tool supports are or may be identical, and only two will bedescribed in detail. The support 4| is mounted on the carriage foradjustment about a vertical axis of suitable means (not shown). Thecarriage 4| is provided with ways 42 in which is mounted a slide 43which carries the tool and its driving mechanism. The slide 43 isprovided with depending lug 44 which is screw threaded to receive athreaded shaft 45, the latter being provided with a squared projectingend 46 for manipulation by .a suitable tool. As will be readilyunderstood, rotation of the shaft 45 provides for adjustment of theslide 43 toward and away The tool T. is mounted on a spindle bushing 41and is adapted to be actuated from motor 48 by suitable drivingconnections received within a housing 49.

As will be seen from Fig. 2. the axis of the tools T are in a planeinclined to the horizontal.

In addition, since these tools are conical, their axes are furtherinclined relative to the axis 'or the work piece in a horizontaldirection. Due to the inclinationof the axes of the tools from ahorizontal plane, the working surface of each tool contacts the axis ofthe work piece W only over a limited area. In order to explain theoperation of this machine and the practice of this,

type of cutting, it may be assumed for the nioment that the motors 3|and 40 are stopped and the motor 48 is energized, thus rotating the toolT. If this tool is adjusted by means of the threaded shaft 45 toward thework piece. it will eventually contact the work piece at a point P.Further feeding of the tool toward the work piece causes the tool to cutinto the work piece and form a shallow rounded scallop therein. Thisscallop, as will be evident, will vary in shape according to the shapeand radius of the curvature of the tool, and the amount which the toolis fed into the work piece. If at this time the motor 32 is started,thus rotating the work piece W, the scallop will be extendedcircumferentially around the work piece, forming a shallow groovetherein, the shapeof which will depend upon the considerationspreviously discussed with reference to the shape of the scallop. If themotor 40 is now energized, resulting in a slow translation of thecarriage 31 in a direction parallel to the axis of the work piece, theshallow groove will be extended in a helical path around the work piece.

convolutions of the helical groove thus formed overlap by a substantialamount. Normally, the.

be evident, upon the shape of the individual The shape of the groovesformed by the tool. groove, as previously stated, depends upon a numberof considerations and depends also, as will be evident, upon the angularrelationship between the axis of the tool and of the work. Thus in orderto obtain the rapid removal of metal and at the same time to obtain asmooth finish on the surface of the work piece, it is necessary tocorrelate the variables referred to. It is impossible, of course, togive a set of rules which will be applicable to all cases but with theforegoing suggestions in mind, those skilled in the art may readilypractice the invention.

I have illustrated in Fig. 7 a work piece 80 corresponding to that shownin Fig. with the central portion thereof cut away on a vertical axialsection to show the action of the cutting tool when operated with itsaxis crossed at a limited angle to'the axis of the work piece. A tool,such as 18 shown in Fig. 5, cuts a groove in the work shown by thescallop Ii in Fig. '7. The groove is of shallow depth and ofconsiderable extent. Furthermore, this scallop in the sectional viewshown in Fig. '7 has a curve which is a substantial distance.

It willbe understood that this scallop, due to V In order to obtain asmooth finish on the work piece it is desirable that adjacent therotation of the work piece, is a section of a groove formed about thework piece. In order to finish the surface of the work piece, therelative feeding motion is introduced between the tool and a work piecewhich will result in distribution of the out along the work piece. Thismay.

be done by relatively translating the tool and work piece in thedirection of the axis of the work piece or transverse thereto underproper conditions. In either case I have illustrated in Fig. 7 theconditions which result from the feeding motion referred to. The dottedline 82 out by a distance d in which d of courseis the same distance asd referred to above. However, it will be noted that the amount ofmaterial removed at the bottom of the cut is very small.

The result of this is that after the tool is fed relative to the work,material 83 is removed by preliminary rough cuts away from the center ofcrossed axis and that adjacent the center of crossed axis the work pieceis accurately finished by cuts of exceedingly fine nature. Therefore,the work piece is finished to a very high degree of accuracy. Inpractice it has been found that the finish imparted is substantially ,amirror finish. v

In the machine shown in Fig. 2, I have illustrated a pair of cuttersoperating on opposite sides of the 'work piece. These cutters may beemployed in various relationships, some of which will be pointed out.The cutter T} may be set so as to take a cut of predetermined cut on thework piece and the cutter T may be set only very slightly in advance ofthe cutter T so that the cutter T in effect acts as a roughing cutterand the cutter T acts as a final finishing cutter, By employing thecutters in this manner, a superior finish may be obtained. On the otherhand the cutters T and T may be set to take a cut of the same depthwhich will result in substantially more metal being removed in a singlepassat the sacrifice of the smoothness of the finished surface.

I have illustrated in Fig. 3, a machine adapted to carry out the methoddisclosed herein, and in this figure a frame 50 is provided with anoverhanging and, in this figure, forwardly projecting head 5| whichcarries a tool support 52. The tool support 52 mounted for a swiveladjustment about a vertical axis on the head 5! for the purpose ofchanging the crossed axis setting of the tool 53 relative to the work54; A motor 55 is carried by the tool support 52 and is adapted torotate the tool 53. Mounted in vertical ways (not shown) to the frame 50is a vertically adjustable table 56. This table may be verticallyadjusted as by a suitable jack screw (not shown) adapted to be actuatedby the hand wheel 51.

Any conventional means of raising and lowering the table may beprovided. Mounted in suitable ways on the table 56 is acarriage 58 whichis adapted to be reciprocated horizontally and from right to left asseen in Fig. 3. Suitable automatic mechanism is preferably provided forreciprocating the carriage and this may take the form of a depending lugand threaded shaft corresponding to the lug l5 and the shaft l'l shownin Fig. l. A motor may be provided for rotating the shaft and this motormay be actuated by a reversing switch 59. A pair of adjustableprojections and BI may be mounted on the carriage and this will reversethe rotation of the motor controlling the translation of the carriage 58and will result in alternate translation or reciprocation of thecarriage 58. The carriage is adapted to support the work piece 54between a power head stock 62 and tail stock 63.

In the embodiment illustrated, both the work piece 54 and the tool 53are cylindrical, and due to the crossed axes relationship, the contactbetween the work piece and the tool will "be over a very small area,depending upon the amount which the table 56 is elevated. As the table56 is elevated, the tool 53 and the work piece 54 come into pointcontact. If the tool 53 is at this time rotating, .iurther elevation ofthe table 56 7 causes a shallow scallop to be cut in the surface of thework piece 34. Upon rotation of the work piece, this scallop will beextended about the periphery of the work piece to forma shallow groovetherein. Slow translation of'the carriage 58 simultaneously with therotation of both tool and work piece will result in a shallow helicalgroove being formed about the work piece,

As in the discussion of the operation of the mechanism illustrated inFig. 2, the shape of the groove cut about'the work piece will dependupon the shape and radius of curvature of the cutter; the shape andradius of curvature of the work piece; the angle at which the axes ofthe cutter and work piece are crossed, and the depthto which the tool isfed into the work piece. In this case as in the case previouslydiscussed, the work piece and the tool will be rotated at speeds whichresult in a desirable cutting relationship between the tool and thework. Depending upon these variables, the carriage 58 is translatedrelatively slowly during the rotation of the tool and work, the rate oftranslation being such that adjacent convolutions of the helical grooveoverlap to an extent which insures accurate finish being imparted to thework piece.

The method as practiced may be varied by a number of additional stepssuch for example as elevating the work piece by predetermined amounts atthe end of each reciprocation, until the work piece is cut tosubstantially the desired size, after which a number of ,finishingpasses maybe made without further feeding.

. As in the preceding example, the finish imparted to the work piecewill be exceedingly fine, for thereason that the cutting is performed atlow tool pressure and at relatively hlgh'speed.

I have illustrated a somewhat different embodiment of mymachine in Fig.4. .In this figure the parts in operation correspond exactly to themachine illustrated in Fig. 3, with the exception that the tool supportwhich is mounted on the head. 66 for swivel adjustment about a verticalaxis, is arranged to support the cutter 61 with its axis inclined to ahorizontal plane. This is for the reason that the cutter 61 asillustrated in this figure is a conical cutter and is adapted in thisinstance to work on a cylindrical work piece- 68. It will be understoodthat the axis of the tool is inclined to the axis of the work piece atan angle which is made up of two angular difierences. In the firstplace, since the tool as illustrated inthis figure is a conical cutterand since the axis of the work piece is shown as horizontal, it isnecessary to incline the axis of the cutter from a horizontal plane byan angle equal to half the vertex angle of the cone. This angularadjustment, if none other were made and if the axis of the work pieceand the cutter were co-planar, would result in line contact between thecutter and the work piece. present method of cutting depends upon thisline contact being supplanted by a contact of limited area. Therefore,in order to carry out the present invention, it is necessary for theswivel head 65 to be rotated about a vertical axis by an amountnecessary to bring about the desired type of contact between the tooland the work.

In this machine a vertically adjustable table 69 is provided and meansactuated by a hand wheel 10 interconnect the support II and the tablefor-elevating the table. A horizontally reciprocable carriage I2 isprovided on the table and as in the embodiment illustrated in Fig. 3, itis contemplated that automatic means will be provided to reciprocate thecarriage in a horizontal plane. The work piece 68 is adapted to berotated by a power head stock 13, being mounted for this purpose betweenthe head stock and a releasable tail stock 14.

In the machines illustrated, the means for distributing the cuttingaction across the surface of the work piece have in each case been shownas means for producing relative reciprocation in the However, the

direction of the axis'of the work piece. It will be understood, however,that relative motion need not be limited to this direction. In Figs. 5and 6 I have illustrated diagrammatically the relationship between acylindrical cutter I8 and 'a cylindrical work piece and a conical cutter"I9 and a cylindrical work piece 8|, respectively. In both cases due tothe crossed axes relationto be finished as previously stated, a relativemotion must be introduced between the work piece and tool. Forsimplicity in the machines previously described in detail, this relativemotion is in the direction of the axis of the work piece. However; thatthis relative motion need not be so limited will be apparent.

Considering first Fig. 5, it will be apparent that bodily motion of thecutter 18 'in a direction perpendicular to the axis of the work piece 80will cause the finishing action of the cutter to be distributed alongthe axis of the cutter. This is for the reason that the finishing actionis limited to a zone as seen in Fig. 5 directly beneath,

the center of crossed axes and as the axis of the cutter is movedupwardly, seen in this figure, the center of crossed axes will shift tothe right. Following this explanation further, it will be seen thatrelative movement between the. cutter and the work piece in anydirection other than parallel to the axis of the cutter will result insome distribution of the finishing action along the work.

Where the relative reciprocation between the parts is in the directionof .the axis of the work, it will be apparent that only a narrow zonearound the cutter will come into action. Y If, on the other hand, thedirectionof relative motion between the cutter and the work is in anydirection other than parallel to the axis of the work or parallelparallel to the axis of the cutter.

- that the cutter effectively envelops the work to the axis of thecutter, the distribution of the finishing action axially of the workwill be accomplished by a corresponding distribution across the face ofthe tool. In many cases this is a desirable feature, since it preventslocalized wear on the tool and this non-parallel relative motion may beadvantageously employed to increase tool life.

In the case illustrated in Fig. 5, when both the work piece and thecutter are cylindrical, the only requirement regarding relative motionbetween the cutter and the work piece is that such relative motion becaused by moving one member in a plane which is parallel to the axis ofthe other. As a matter of fact, this limitation is a practicalconsideration only since it is apparent that distribution of thefinishing action could be accomplished by moving the cutter or the toolin a curved path about the axis of the other. While this last istheoretically possible, it oflers no practical advantages and thedisadvantages of constructing the machine to provide such motions areobvious.

In connection with the diagram shown in Fig.

6, the same consideration as previously discussed applies, except thatsince the axis of the cutter is inclined to the axis of the work by anadditional amount to compensate for the cone angle of the cutter, therelative motion between the parts may not be defined as simply producedby moving one of the parts parallel'to the axis of the other. Thefinishing action may be distrib uted along the work piece by moving thecutter in -a plane parallel to the axis of the work, and this motion maybe in the direction of the axis of the work or pendicular to the. axisof the work, or in fact any direction other than This same relativemotion may, of course, be produced by moving the work in the samedirection;

It will be apparent that the same method of cutting may be employed tocut a conical part,

the only change being that the direction of relative motion between thework piece and tool shall be such that the finishing action isdistributed uniformly over the work piece. Similarly, the same method ofcutting may be employed in cutting the work piece having a surface ofrevolution generated by the curved line and this will be true,whether'the surface of revolution is concave or convex. It is onlynecessary that the dimensionsof the cutter be chosen so that they mayfollow the desired contour without interference.

In all cases the same essential relationship exists, that is, a rotarycutter contacting a rotatingwork piecewith their axes so arranged thatthe contact between the two is limited to a relatively small area and arelative motion is introduced between the two such that the finishingaction is distributed uniformly across the surface of the ures, thecutters are provided with helically arranged cutting edges, although in'this type of work this is by no means essential. i

It is further possible to finish a work piece such as shown in Fig.5,for example, by employ,-

' 'ing a rotary cutter having a concaved, working surface. If theconcavity is selected relative to the diameter and cross axialrelationship such piece from side to side of the cutter, the benefits ofmy improved type of cutting disappear. However, if the concavity of thetool is described from a greater radius so that while the area ofcontact is somewhat enlarged, it still remains relatively small, thesame advantages previously pointed out are inherent. i

The foregoing detailed description has been given for clearness ofunderstanding only, and no unnecessary limitations should be understoodtherefrom, but the appended claims should be construed as broadly aspermissible in view of the prior art.

What I claim as my invention is:

1. The method of finishing a work piece having a circular cross-sectionsurface of revolution comprising rotating said work piece in contactwith a rotary tool with the axes of said work piece and toolnon-intersecting and crossed, relatively moving said tool and work piecein a direction to distribute the finishing action over the surface ofsaid work piece, while maintaining the axes of saidtool and work piecerigidly spaced.

.2. The method of finishing a work piece having a circular cross-sectionsurface of revolution comprising rotating said work piece in contactwith a rotary tool with the axes of said work piece and toolnon-intersecting and crossed, relatively reciprocating said tooland workpiece in a direction to distribute the finishing action over the surfaceof said work piece, while maintaining the axes of said tool and workpiece rigidly spaced, and

feeding said tool and work piece together at the end of eachreciprocation by a predetermined increment.

3. The method of finishing a work piece having a circular cross-sectionsurface of revolution comprising rotating said work piece in contactwith a rotary tool with the axes of said work piece and toolnon-intersecting and crossed, relatively moving said tool and work piecein a plane parallel to the plane tangent to the surface of the workpiece at the point of finishing.

4. The method of finishing a work piece having a non-planar surface ofrevolution generated by rotating a straight line about an axis coplanarwith said line, comprising providing a tool having a cutting surfacedefining a non-planar surface of revolution generated by rotating astraight line about an axis coplanar with said line, positioning saidtool and work piece in contact with their axes non-intersecting andcrossed, rotating said tool and work piece, and relatively moving saidtool and work piece in a direction to distribute the cutting action overthe surface of said work piece.

. 5. The method of finishing a work piece having a circularcross-section surface of revolution providinga rotary tool having aworking surface defining a circular cross-section surface of revolution,positioning said tool and work piece in contact at crossed,non-intersecting axes and rotating said tool so that said tool isadapted to\cut a small scallop in the surface of said work piece,rotating said work piece so that a shallow groove is cut around saidwork piece, and simultaneously relatively moving said tool and workpiece so that the. finishing action is distributed along the surface ofsaid work piece.

6. The/ method of finishing a work piece having' a circularcross-section surface of revolution providing. a rotary tool having aworking surface defining a circular cross-section surface of revolution,positioning said tool and work piece in contact at crossednon-intersecting axes and rotating said tool so that said tool 'isadapted to cut a small scallop in the surface of said work piece,rotating said work piece so that a shallow groove is cut around saidwork piece, and simultaneously relatively moving said tool and workpiece so that said groove is formed spirally along said work piece, therate of rotation of said work piece being so proportioned to saidrelative movement that the convolutions of said groove overlap.

7. The method of finishing a work piece having a convex surface ofrevolution comprising in an overlapping helix.

8. The method of finishing a work piece having a surface of revolutionwhich comprises: ro-

tating the work piece, rotating a tool having a working surface ofrevolution in contact with the work piece with their axesnon-intersecting and crossed at a limited angle, and relatively feedingsaid tool andwork piece to distribute the finishing action along saidwork piece so as to take roughing cuts followed by finishing cuts on thework piece.

9. The method of finishing a cylindrical work piece, with a cylindricaltool, which comprises positioning said tool in contact with said workwith their axes in spaced parallel planes, and inclined to each other insaid parallel planes. at a limited angle, rotating said tool and workindependently, and relatively feeding said tool and work in a planeparallel to the axes of both tool and work.

10. The method of finishing a cylindrical work piece with a conicaltool, which comprises contacting said work and tool with their axesrelated in a compound angle made up of an inclination in the plane ofthe axis of the work equal to sub- 'azoacva cutter, and a limitedinclination in a plane perpendicular to said first plane, rotating saidtool and work and relatively feeding said tool and work along the work.

11. The method of finishing a work piece having a surface of revoluiongenerated by a straight line element, with a rotary cutter having a.working surface of revolution generated by a straight line element,which comprises contacting said that the instantaneous direction ofmotion of said surfaces at the zone of contact are along lines whichdiverge by a limited angle.

13. The method of finishing a workpiece having a circular cross-sectionsurface of revolution, with a rotary tool having a circularcross-section surface of revolution, which comprises rotating said tooland work in surface contact with their axes non-intersecting andangularly related so that said tool removes metal around said work inthe form of a relatively wide, very shallow curved groove, andrelatively feeding said tool and work in a direction along said work toform said groove as a substantially overlapping helix.

' 14. A machine for finishing a work piece having a surface ofrevolution which comprises means for rotating a, work piece about itsaxis, means for rotating a rotary cutter in contact with the surface ofsaid work, with the axes of said cutter and work in no common plane andcrossed at a limited angle, and means for relatively moving said cutterand work to distribute 4 said cut along the work.

ROBERT s. DRUMMOND.

